The Spectral Theorem for Self-Adjoint Operators

The Spectral Theorem for Self-Adjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing a functional calculus that extends the intuitive notion of evaluating a polynomial on an operator. The Spectral Theorem is fundamentally important to operator theory and has applications in many fields, especially harmonic analysis on locally compact abelian groups. This thesis represents a merging of two traditional treatments of the Spectral Theorem and includes an extended example highlighting an important application in harmonic analysis

Why Waste The Wind? A Look into Small Scale Wind Energy

The human race’s dependence on fossil fuels for energy generation has started to cause major changes in the environment. Climate change is a universal issue and it is evident that our current energy schematic is not sustainable. At the University of Massachusetts, small-scale wind power has the potential to be a key component in UMass’ energy portfolio as the university shifts from reliance on fossil fuels to renewable energy. Strategically placed turbines would produce clean, renewable energy, reduce greenhouse gas emissions, and help to decentralize energy dependence on the Central Heating Plant. Small-scale turbines, like the eddyGT, are tested technologies that show promise for on-campus applications. In addition to starting UMass’ transition to renewable energy, monetary savings from wind-energy investment could even be put towards future renewable energy endeavors. And, though current turbine technology suffers from limited energy production capabilities, this issue is addressed by high altitude turbines which access stronger and more consistent winds. While still in the process of development, high altitude wind turbines have the potential to be an important renewable energy source in the future. Implementation of small scale wind energy at UMass will require research on wind speeds throughout campus. This data will facilitate determination of ideal locations and types of small-scale wind turbines for the campus, the first step in achieving UMass’ independence from fossil fuels

Diversity and Distribution of the Asilidae in Ohio

Asilidae are important predatory insects that eat other insects. To understand their diversity, abundance, and habitat associations in Ohio, passive water bowl traps were set across 149 sites in Ohio from May to October 2020 by volunteer community scientists. All specimens were sent to the Goodell laboratory at The Ohio State Newark to be pinned and identified. A total of 1,705 asilid specimens were collected representing 25 species. The most common species was Atomosia puella, which accounted for 80% of all specimens. To understand habitat influences on abundance and diversity, the presence of forest, grassland/shrub, cropland, and developed land in a 500 m buffer around each site was calculated. These landscape variables were analyzed to determine which habitat was most important for overall Asilidae species richness and abundance. Both cropland and developed land were associated with a decrease in Asilidae abundance and species richness. Forested habitat was positively associated with species richness. Grasslands and open landscapes were positively associated with abundance, largely due to the increase in Atomosia puella abundance with the percent of open habitat. Asilid diversity was not significantly associated with grassland or open habitat. The anthropogenic factors of cropland and developed land negatively influence Asilidae potentially because of pesticides and habitat damage, suggesting the need for conservation management. Forested areas contain greater habitat heterogeneity than grasslands, potentially contributing to the increase in species richness. These findings provide insight into the distribution of Asilidae within Ohio and contribute to future conservation management.Ohio Biodiversity Conservation Partnership grant through the Ohio Department of Natural Resources to Dr. Karen Goodell.Arts and Sciences Undergraduate Research ScholarshipNo embargoAcademic Major: Biochemistr

Different but the Same: Common Themes in Illness Experience Among People With Diverse Long COVID Symptoms and the Potential Benefits of Virtual Group Medical Visits

Long coronavirus disease 2019 (COVID-19) is poorly understood, widespread and debilitating. Integrative medical group visits (IMGVs) provide group medical care virtually or in person and are reimbursed by insurance payors. IMGV introduces integrative modalities such as mindfulness, nutrition, and acupressure in a person-centered, supportive, and educational environment. To evaluate a telehealth IMGV program called Nourish to Flourish (N2F) for patients with long COVID, three researchers conducted a qualitative analysis of pre- and post-group individual interviews. Twenty-five patients provided interviews, of which fifteen included pre- and post-group individual interviews. Main themes were unpredictable symptom patterns, a common range of emotions associated with long COVID experience, reconceptualizing self-identity, multiple barriers to care in conventional settings, and connections formed in N2F. Although symptoms varied, N2F participants found commonalities in their experiences of living with long COVID. They empathized with one another regarding changing symptoms, inconsistent social support, shifting identities, and barriers to effective medical care